Milnor Fibrations and Regularity Conditions for Real Analytic Mappings

Abstract

When ƒ: (Rn,0)(Rn,0)→(Rp,0)(Rp,0)is a surjective real analytic map with isolated critical value, we prove that the(m)-regularity condition (in a sense we define) ensures that f||f||f||f|| is a fibration on small spheres, ƒ induces afibration on the tubes and these fibrations are equivalent.In particular, we make the statement of [12] more precise in the case of an isolated critical point and weextend it to the case of an isolated critical value.